> there is no nginx.core file found in /home/core/ , thats the path specified
> in nginx.conf

Make sure:
- /home/core/ is writable (chmod a+w)
- ulimit is configured correctly
- fs.suid_dumpable is ok?

You can read more about it here:
http://www.cyberciti.biz/tips/linux-core-dumps.html
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